Heat a large skillet oven medium heat and add olive oil. Toss in shredded brussels sprouts and garlic with salt and pepper to taste (I like a lot!) and red pepper flakes, tossing to coat. Cook until wilted and browning, stirring occasionally, about 5-6 minutes. Remove sprouts from the skillet and place them in a bowl.
Heat the same skillet (or a separate griddle, etc) oven medium-low heat. Butter the outsides of every bread slice, then layer the sandwiches with slices of cheese, the brussel sprouts, a good drizzle of balsamic glaze and more cheese. Top off with a slice of bread, buttered-side up. Cook until each side is golden and crisp and cheese is melted, then gently flip and do the same.